I'm having problems converging the Pressure-Correction equation using SIMPLE in parallel for incompressible flows I am using the AMG solver and the same case converges in serial. Somewhere, I read that introducing a compressibility factor (beta) might help in convergence but couldnot find any literature. Could anyone help me as to how to calculate the factor based on current values of pressure rather than simply assuming 0.01 - 0.05 of Ap as mentioned in Peric.

If your code converges in serial mode but not in parallel mode then I don't think your problem is going to be solved by changing your under-relaxation. It sounds like you have some communication issues. Have you validated your parallelization against any other simple problems?